Torpedo Data Computer

The Torpedo Data Computer (TDC) was an early electromechanical analog computer used for torpedo fire-control on American submarines during World War II (see Figure 1). Britain, Germany, and Japan also developed automated torpedo fire control equipment, but none were as advanced as US Navy's TDC. cite book
last = Friedman
first = Norman
title = US Submarines Through 1945: An Illustrated Design History
year = 1995
publisher = Naval Institute Press
isbn=1-55750-263-3
pages = p. 195
quote = No other navy developed a comparable instrument [to the TDC] . The Germans and Japanese used angle solvers without position keepers (at least in the Japanese case, the device also had a timer that allowed it to dead reckon target position for indirect fire through smoke or mist). Probably because the Japanese had no TDC, they abandoned stern torpedo tubes in their later cruiser and fleet submarines on the grounds that they would require excessive gyro angles. ] These nations all developed torpedo fire control computers for calculating torpedo courses to intercept targets, but the TDC added the ability to automatically track the target. The target tracking capabilities of the TDC were unique for submarines during WWII and set the standard for submarine torpedo fire control at that time.cite web
title = Analog Computers
work = Lexikon's History of Computing
date = 1995
url = http://www.computermuseum.li/Testpage/AnalogComputers.htm#Restoration
accessdate = 2006-07-03 ] While the TDC's target tracking abilities were unique for submarine torpedo fire control during WWII, target tracking was used on surface ship torpedo fire control systems by a number of nations (see references in this article to [http://www.hnsa.org/doc/destroyer/ddfc/index.htm US destroyer] and [http://www.fischer-tropsch.org/primary_documents/gvt_reports/USNAVY/USNTMJ%20Reports/USNTMJ-200F-0086-0124%20Report%20O-32.pdf Japanese torpedo fire control] ). The TDC was the first analog computer to miniaturize the capability enough for deployment on a submarine.]

The TDC was designed to provide fire-control solutions for submarine torpedo launches against ships running on the surface (surface warships used a [http://www.hnsa.org/doc/destroyer/ddfc/index.htm different computer] for their torpedo launches). The TDC had a wide array of [http://www.fleetsubmarine.com/tdc.html dials and switches] for data input and display. To generate a fire control solution, it required inputs on

* submarine course and speed, which were read automatically from the submarine's gyrocompass and pitometer log
* estimated target course, speed, and range information (obtained using data from the submarine's periscope, [http://www.bowfin.org/website/bowfin/bowfin_systems/TBT/tbt.htm target bearing transmitter] , radar, and sonar observations)
* torpedo type and speed (type was needed to deal with the different torpedo ballistics)

The TDC performed the trigonometric calculations required to compute a target intercept course for the torpedo. It also had an electromechanical interface to the torpedoes that allowed it to automatically set the torpedo courses while they were in their tubes, ready to be launched.

The TDC's target tracking capability was used by the fire control party to continuously update the fire control solution to the torpedoes even while the submarine was maneuvering. The TDC's target tracking ability also allowed the submarine to accurately launch torpedoes even when the target was temporarily obscured by smoke or fog.

The TDC was a rather bulky addition to the sub's conning tower and required two extra crewmen: one as an expert in its maintenance, and the other as its actual combat operator. Despite these drawbacks, the use of the TDC was an important factor in the successful commerce raiding program conducted by American submarines during the Pacific campaign of WWII. First-person accounts published on the American submarine campaign in the Pacific often cite the use of TDC.cite book
last = O'Kane
first = Richard
title = Clear The Bridge:The War Patrols of the U.S.S. Tang
publisher = Bantam Books
date = 1977
location = New York
ISBN= 0-553-14516-9] cite book
last = O'Kane
first = Richard
title = Wahoo: The Patrols of America's Most Famous World War II Submarine
publisher = Bantam Books
date = 1987
location = New York
isbn= 0-553-28161-5]

Two upgraded US Navy WWII-era fleet submarines (USS Tusk and USS Cutlass) with their TDCs continue in service with Taiwan's navy and US Nautical Museum staff are assisting them with maintaining their equipment [cite web|url=http://www.maritime.org/taiwan/index.htm|title=Museum documents an operating US, WW II built submarine in Taiwan.|accessdate=2008-07-13] . The museum also has a fully restored and functioning TDC for the USS Pampanito, docked in San Francisco.

Background

History

The problem of aiming a torpedo has occupied military engineers since Robert Whitehead developed the modern torpedo in the 1860s. These early torpedoes ran at a preset depth on a straight course (consequently they are frequently referred to as "straight runners"). This was the state of the art in torpedo guidance until the development of the homing torpedo during the latter part of World War II. There were other forms of torpedo guidance attempted throughout WWII. Notable are the Japanese human-guided "Kaiten" and German pattern running and acoustic homing types for attacking convoys. Today, most submarine-launched torpedoes are wire-guided with terminal homing guidance.] The vast majority of the torpedoes launched during WWII were straight running torpedoes and these continued in use for many years after WWII. For example, the standard U.S. WWII torpedo remained in service until 1980 and still serves with foreign navies today.cite web
url = http://www.geocities.com/Pentagon/1592/ustorp5.htm
title= Part Five: Post WW-II Submarine Launched/ Heavyweight Torpedoes
accessdate=2006-07-26
author= Frederick J Milford
date= October 1997
format= HTML
work= US Navy Torpedoes] In fact, two WWII-era straight running torpedoes, fired by nuclear powered submarine HMS "Conqueror" sank the ARA "General Belgrano" in 1982, the last ship sunk by a submarine in combat to date.

During World War I, computing a target intercept course for a torpedo was a manual process where the fire control party was aided by various slide rulescite web
title = Torpedo Data Computer
work = FleetSubmarine.com
date = 2002
url = http://www.maritime.org/tdc.htm
accessdate = 2006-07-03 ] (the U.S. examples were colloquially called "banjo", for its shape, and "Is/Was") and clever mechanical sights.cite web
title = Firing a Torpedo Using A Mechanical Computing Sight
work=The Dreadnaught Project/sim
url =http://www.dreadnoughtproject.org
date=2000
accessdate=2006-07-11] During World War II, [http://www.msichicago.org/exhibit/U505/virtualtour/photo_tour/contower.html Germany] , [http://web.ukonline.co.uk/chalcraft/sm/attack.html Britain] , Japan, and the United States each developed analog computers to automate the process of computing the required torpedo course,cite book
last = Jackson, USNR
first = Lt.(jg) J.G.
url=http://www.fischer-tropsch.org/primary_documents/gvt_reports/USNAVY/USNTMJ%20Reports/USNTMJ-200F-0086-0124%20Report%20O-32.pdf
title = Japanese Torpedo Fire Control
date = February, 1946
publisher = US Naval Technical Mission to Japan
id = Fascicle O-1, Target O-32
quote = The Japanese spent considerable effort on the design and manufacture of torpedo fire control equipment. The various units were well constructed and function with good accuracy. their submarine torpedo data computers and auxiliary equipment were more simplified and less accurate than US equipment, while above water torpedo control gear (especially for cruisers) is more complicated and equal in merit to that of U.S. design.
format=PDF] ). The first US submarine designed to use the TDC was the USS Tambor,cite web
last = Mohl
first = Michael
title = Tambor (SS-198)
work = NavSource Online: Submarine Photo Archive
date = 2006
url = http://www.navsource.org/archives/08/08198.htm
accessdate = 2006-08-01 ] which deployed in 1940 with the [http://www.maritime.org/tdc.htm Torpedo Data Computer TDC Mk III] (see Figure 1). In 1943, the [http://www.usscod.org/tdc.html Torpedo Data Computer Mk IV] was developed to add support for the Torpedo Mk 18.The [http://www.microworks.net/pacific/armament/mk18_submarine.htm Torpedo Mk 18] was an electric torpedo and therefore wakeless and difficult for surface forces to trace. On the downside, it was slower than the Mk 14. This made it more difficult to aim accurately because larger gyro angles were involved. Even so, thousands of them were launched during WWII. ] cite book
last = O'Kane
first = Richard
title = Clear The Bridge:The War Patrols of the U.S.S. Tang
publisher = Bantam Books
date = 1977
location = New York
pages = p. 221
quote = ...Mk 18-1 electric torpedoes. They were slower, convert|27|kn|km/h|0 instead of the convert|46|kn|km/h|0 of our steam torpedoes, but only the twist of a knob on the TDC was enough to throw in the proper cam so they would take the correct lead angle.
id = ISBN= 0-553-14516-9] and semi-automatic use of radar data. Both the TDC Mk III and Mk IV were developed by [http://www.google.com/search?q=cache:JcKzqQs3rPAJ:www.armahistory.com/+&hl=en&gl=us&ct=clnk&cd=1 Arma Corporation] (now American Bosch Arma).

The Problem of Aiming a Straight Running Torpedo

A straight running torpedo has a gyroscope-based control system that ensures that the torpedo will run a straight course. The torpedo can run on a course different from that of the submarine by adjusting a parameter called the gyro angle, which sets the course of the torpedo relative to the course of the submarine (see Figure 2). The primary role of the TDC is to determine the gyro angle setting required to ensure that the torpedo will strike the target.

Determining the gyro angle required the real-time solution of a complex trigonometric equation (see Equation 1 for a simplified example). The TDC provided a continuous solution to this equation using data updates from the submarine's navigation sensors and the TDC's target tracker. The TDC was also able to automatically update all torpedo gyro angle settings simultaneously with a fire control solution, which improved the accuracy over systems that required manual updating of the torpedo's course. cite book
last = Friedman
first = Norman
title = US Submarines Through 1945: An Illustrated Design History
year = 1995
publisher = Naval Institute Press
isbn=1-55750-263-3
pages = p. 196
quote = Once the data seemed to match (i.e., once it appeared that the target track angle was correct),the TDC operator passed it to an angle solver, a torpedo ballistic computer, that remotely set torpedoes through power gyro setters at the tubes. As the submarine maneuvered, her torpedoes were kept properly aimed: a submarine evading escorts could still expect to hit the target. ]

The TDC enables the submarine to launch the torpedo on a course different from that of the submarine, which is important tactically. Otherwise the submarine would need to be pointed at the projected intercept point in order to launch a torpedo.Torpedoes were developed by the United States with this capability during WWI. However, without automated fire control it was difficult to realize the full advantages of this approach.] Requiring the entire vessel to be pointed in order to launch a torpedo would be time consuming, require precise submarine course control, and would needlessly complicate the torpedo firing process. The TDC with target tracking gives the submarine the ability to maneuver independently of the required target intercept course for the torpedo.

As is shown in Figure 2, in general, the torpedo does not actually move in a straight path immediately after launch and it does not instantly accelerate to full speed, which are referred to as torpedo ballistic characteristics. The ballistic characteristics are described by three parameters: reach, turning radius, and corrected torpedo speed. Also, the target bearing angle is different from the point of view of the periscope versus the point of view of the torpedo, which is referred to as torpedo tube parallax.cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = 1-12
chapter = Definitions
accessdate = 2006-08-22 ] These factors are a significant complication in the calculation of the gyro angle and the TDC must compensate for their effects.

Straight running torpedoes were usually launched in salvo (i.e. multiple launches in a short period of time)cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = 1-9
chapter = Definitions
quote = A number of torpedoes fired at short-intervals at the same target.
accessdate = 2006-08-22 ] or a spread (i.e. multiple launches with slight angle offsets)cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = 1-9
chapter = Definitions
quote = Offset angle or change in target bearing applied to the gyro angle order of each torpedo of a salvo to cause successive torpedoes to hit at different points along the target length or track extended. NOTE: An offset angle is used in a divergent spread, whereas the linear spread in a longitudinal spread is accomplished by changing the point of aim.
accessdate = 2006-08-22 ] to increase the probability of striking the target given the inaccuracies present in the measurement of angles, target range, target speed, torpedo track angle, and torpedo speed. Salvos and spreads were also launched to strike tough targets multiple times to ensure their destruction.cite book | title = Current Doctrine Submarines
editor = Commander Submarine Force, Pacific Fleet
title = Current Submarine Doctrine
origdate = 1944-02
date = 2006-02-17
format = html
pages = paragraph 4614
chapter = Attacks -- General (Chapter IV, Section 1)
chapterurl = http://www.history.navy.mil/library/online/ss-doc-4.htm
url = http://www.history.navy.mil/library/online/sub_doctrine.htm
accessdate = 2006-07-02 ] The TDC supported the launching of torpedo salvos by allowing short time offsets between firings and torpedo spreads by adding small angle offsets to each torpedo's gyro angle. The last ship sank by a submarine torpedo attack, the ARA Belgrano, was struck by two torpedoes from a three torpedo spread.cite web
url = http://www.geocities.com/nmdecke/Submarines.html
title = Submarines 1950-2000, a study in unused potential
accessdate = 2006-08-20
author = Nathan Decker
date = 2005-07
format = html ]

To accurately compute the gyro angle for a torpedo in a general engagement scenario, the target course, range, and bearing must be accurately known. During WWII, target course, range, and bearing estimates often had to be generated using periscope observations, which were highly subjective and error prone. The TDC was used to refine the estimates of the target's course, range, and bearing through a process of
* estimate the target's course, speed, and range based on observations.
* use the TDC to predict the target's position at a future time based on the estimates of the target's course, speed, and range.
* compare the predicted position against the actual position and correct the estimated parameters as required to achieve agreement between the predictions and observation. Agreement between prediction and observation means that the target course, speed, and range estimates are accurate.

Estimating the target's course was generally considered the most difficult of the observation tasks. The accuracy of the result was highly dependent on the experience of the skipper. During combat, the actual course of the target was not usually determined but instead the skippers determined a related quantity called "angle on the bow." Angle on the bow is the angle formed by the target course and the line of sight to the submarine. Some skippers, like the legendary Richard O'Kane, practiced determining the angle on the bow by looking at IJN ship models mounted on a calibrated lazy Susan through an inverted binocular barrel. cite book
last = O'Kane
first = RIchard H.
title = Wahoo: The Patrols of America's Most Famous World War II Submarine
origyear = 1987
accessdate = 2006-10-22
edition = Bantam
year = 1989
publisher = Bantam
location = New York
isbn= 0-553-28161-5
pages = pp. 108-109
chapter = Part 4: Chapter 1
quote =The opportunity and sharing of responsibility was new within our submarine forces. I answered with a simple, 'I appreciate your confidence, Captain,' and I told him I was off to Sperry to make a lazy Susan for our ship models. I would need them to sharpen the ability to call angles on the bow quickly and accurately ... Through one barrel of a pair of 7x35 binoculars inverted, I called angles from the pantry scuttle on a realistic target. ]

To generate target position data versus time, the TDC needed to solve the equations of motion for the target relative to the submarine. The equations of motion are differential equations and the TDC used mechanical integrators to generate its solution.cite web
last = Bromley
first = Allan
title = Analog Computing Devices
work = Computing Before Computers
ed = William Aspray
date = 1990
url = http://ed-thelen.org/comp-hist/CBC.html
accessdate = 2006-07-22 ]

The TDC needed to be positioned near other fire control equipment to minimize the amount of electromechanical interconnect. Because submarine space within the pressure hull was limited, the TDC needed to be as small as possible. On WWII submarines, the TDC and other fire control equipment was mounted in the conning tower, which was a very small space.cite video
people = Wise, Robert (Director-One scene shows how cramped a conning tower could be.)
year = 1958
title = Run Silent, Run Deep
medium = Film
location = Pacific Ocean] The packaging problem was severe and the performance of some early torpedo fire control equipment was hampered by the need to make it small. cite book
last = Friedman
first = Norman
title = US Submarines Through 1945: An Illustrated Design History
year = 1995
publisher = Naval Institute Press
isbn=1-55750-263-3
pages = p. 350
quote = It [TDC Mk 2] proved ineffective because Ford had to make some massive assumptions about the fire control problem to shrink its size. ]

TDC Functional Description

Since the TDC actually performed two separate functions, generating target position estimates and computing torpedo firing angles, the TDC actually consisted of two types of analog computers:

* Angle Solver: This computer calculates the required gyro angle. The TDC had separate angle solvers for the forward and aft torpedo tubes.
* Position Keeper: This computer generates a continuously updated estimate of the target position based on earlier target position measurements.cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = 4-2
chapter = Chapter 4: The Torpedo Fire Control Party
quote = he TDC Operator is an officer whose station is in the conning tower at the position keeper section of the TDC. His primary duty is to operate the position keeper and, using all available information, obtain the most accurate values of target course, speed, and range that can be determined.
accessdate = 2006-08-22 ]

Angle Solver

The exact equations implemented in the angle solver have not been published in any generally available reference. However, the Submarine Torpedo Fire Control Manual cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
accessdate = 2006-08-22 ] does discuss the calculations in a general sense and a greatly abbreviated form of that discussion is presented here.

The general torpedo fire control problem is illustrated in Figure 2. The problem is made more tractable if we assume:
* The periscope is on the line formed by the torpedo running along its course
* The target moves on a fixed course and speed
* The torpedo moves on a fixed course and speed

As can be seen in Figure 2, these assumptions are not true in general because of the torpedo ballistic characteristics and torpedo tube parallax. Providing the details as to how to correct the torpedo gyro angle calculation for ballistics and parallax is complicated and beyond the scope of this article. Most discussions of gyro angle determination take the simpler approach of using Figure 3, which is called the torpedo fire control triangle. Figure 3 provides an accurate model for computing the gyro angle when the gyro angle is small, usually less than < 30^o.cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = pp. 8-8, 8-9
chapter = Theory of Approach and Attack
quote = Torpedo firing in which small gyro angles (less than 30 degrees) are used is considered to be "Straight Fire" ... The greatest advantage of straight fire (small gyro angles) is that errors in torpedo run have no appreciable effect on the solution. Therefore, when the range is inaccurate, as in stadimeter and telemeter scale approaches, the submarine must maneuver for a small gyro angle shot.
accessdate = 2006-08-19 ] The effects of parallax and ballistics are minimal for small gyro angle launches because the course deviations they cause are usually small enough to be ignorable. US submarines during WWII preferred to fire their torpedoes at small gyro angles because the TDC's fire control solutions were most accurate for small angles. cite book
editor = Commander Submarine Force, Pacific Fleet
title = Current Submarine Doctrine
origdate = 1944-02
url = http://www.history.navy.mil/library/online/sub_doctrine.htm
format = html
accessdate = 2006-08-19
publisher = Department of the Navy
date = 2006-02-17
id = USF 25(A)
pages = paragraph 4509
chapter = Attacks -- General (Chapter IV, Section 1)
chapterurl = http://www.history.navy.mil/library/online/ss-doc-4.htm
quote = The best chances of hitting are with small gyro angles. ]

The problem of computing the gyro angle setting is a trigonometry problem that is simplified by first considering the calculation of the deflection angle, which ignores torpedo ballistics and parallax.cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = pp. 1-2
chapter = Definitions
quote = [Deflection angle is] the angle between the periscope angle and the component of the gyro angle of the torpedo determined only by track angle, torpedo speed, and target speed. See Plate I, figure 3. NOTE The excluded portion of the gyro angle is that due to the tactical characteristics of the torpedo and the torpedo tube parallax.
accessdate = 2006-08-19 ] For small gyro angles, θ_Gyro ≈ θ_Bearing - θ_Deflection. A direct application of the law of sines to Figure 3 produces Equation 1.

(Equation 1)

$frac\{left\; Vert\; v\_\{Target\}\; ight\; |\; \}\{\; sin(\; heta\_\{Deflection\})\; \}\; =\; frac\{left\; Vert\; v\_\{Torpedo\}\; ight\; |\; \}\{\; sin(\; heta\_\{Bow\})\; \}$

where:v_Target is the velocity of the target.:v_Torpedo is the velocity of the torpedo.:θ_Bow is the angle of the target ship bow relative to the periscope line of sight.:θ_Deflection is the angle of the torpedo course relative to the periscope line of sight.

Observe that range plays no role in Equation 1, which is true as long as the three assumptions are met. In fact, Equation 1 is the same equation solved by the mechanical sights of [http://www.history.navy.mil/photos/images/h41000/h41761.jpgsteerable torpedo tubes] used on surface ships during WWI and WWII. Torpedo launches from steerable torpedo tubes meet the three stated assumptions well. However, an accurate torpedo launch from a submarine requires parallax and torpedo ballistic corrections when gyro angles are large. These corrections require knowing range accurately. When the target range was not known accurately, torpedo launches requiring large gyro angles were not recommended.cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = p. 8-10
chapter = Chapter 8: Theory of Approach and Attack
quote = This [ballistic and parallax] correction is automatically computed in the angle solver section of the TDC. This correction varies with torpedo run ... In order to have a correct solution of torpedo run it is mandatory that an accurate range be available.
accessdate = 2006-08-21 ]

Equation 1 is frequently modified to substitute track angle for deflection angle (track angle is defined in Figure 2, θ_Track=θ_Bow+θ_Deflection). This modification is illustrated with Equation 2.

(Equation 2)

$frac\{left\; Vert\; v\_\{Target\}\; ight\; |\; \}\{\; sin(\; heta\_\{Deflection\})\; \}\; =\; frac\{left\; Vert\; v\_\{Torpedo\}\; ight\; |\; \}\{\; sin(\; heta\_\{Track\}-\; heta\_\{Deflection\})\}$

where:θ_Track is the angle between the target ship's course and the submarine's course.

A number of publicationscite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = p. 8-9
chapter = Chapter 8: Theory of Approach and Attack
quote = The optimum torpedo track angle for a convert|16|kn|km/h|0|sing=on target for a convert|46|kn|km/h|0|sing=on torpedo is about 110 degrees and for a convert|29|kn|km/h|0|sing=on torpedo about 125 degrees.
accessdate = 2006-08-19 ] cite book
last = O'Kane
first = Richard
title = Clear The Bridge:The War Patrols of the U.S.S. Tang
publisher = Bantam Books
date = 1977
location = New York
chapter = Part V, Chapter 3
page = p. 303
isbn= 0-553-14516-9
quote = We should have had hits; at least two of them. With an average torpedo track of 110 degrees - torpedoes coming in 20 degrees abaft the beam -- large variations in the enemy's course would result in practically the same lead angle.] state the optimum torpedo track angle as 110^o for a Torpedo Mk 14 (46 knot weapon). Figure 4 shows a plot of the deflection angle versus track angle when the gyro angle is 0^o (i.e. θ_Deflection=θ_Bearing). Most work on computing intercept angles is done using track angle as a variable. This is because track angle is a strictly a function of the target's course and speed along with the torpedo's course and speed. It removes the complexities associated with parallax and torpedo ballistics.] Optimum track angle is defined as the point of minimum deflection angle sensitivity to track angle errors for a given target speed. This minimum occurs at the points of zero slope on the curves in Figure 4 (these points are marked by small triangles). The curves show the solutions of Equation 2 for deflection angle as a function of target speed and track angle. Figure 4 confirms that 110^o is the optimum track angle for a convert|16|kn|km/h|0|sing=on target, which would be a common ship speed.cite book
editor = Commander Submarine Force, United States Atlantic Fleet
title = Submarine Torpedo Fire Control Manual
origdate = 1950-02
date = 2006-04-16
url = http://www.hnsa.org/doc/attack/index.htm
format = html
pages = p. 5-25
chapter = Chapter 5: Duties of the Fire Control Party
quote = In lieu of a better estimate, an initial analyzing speed of convert|15|kn|km/h|0, which is a good average speed determination is to be used.
accessdate = 2006-08-19 ]

There is fairly complete documentation available for a Japanese torpedo fire control computer that goes through the [http://home.comcast.net/~mbiegert/Work/HistOfTech/TDC/Model.htm details of correcting for the ballistic and parallax factors] . While the TDC may not have used the exact same approach, it was likely very similar.

Position Keeper

As with the angle solver, the exact equations implemented in the position keeper have not been published in any generally available reference. However, similar functions were implemented in the rangekeepers for surface ship-based fire control systems. For a general discussion of the principles behind the position keeper, see Rangekeeper.

Notes and references

External links

* [http://www.maritime.org/tdc.htm USS Pampanito: Article on the Pampanito's TDC.]
* [http://www.subsim.com/radioroom/showthread.php?t=94608&page=2 Torpedo Gyro Angle Slide Rules: Plans for making your own.]
* [http://www.enemybeneath.com/mast.htm Masthead Height: Data used by submarine captains in conjunction with the periscope's telemeter to estimate target range.]
* [http://web.mit.edu/STS.035/www/PDFs/Newell.pdf Analog Computing History: Nice survey article on the work of Ford and Newell, early pioneers in analog computing. ]
* [http://www.dreadnoughtproject.org/sim/ WWI Torpedo Fire Control: First-rate simulation illustrating torpedo fire control methods used during WWI.]
*.
* [http://www.bergall.org/320/patrol/torpedo.html US Torpedo History: Good description of operational use of the Mk 14, Mk 18, and Mk 23]
* [http://home.comcast.net/~mbiegert/Work/HistOfTech/TDC/Model.htm Discussion of the torpedo ballistic and parallax corrections used by the Imperial Japanese Navy]